We investigate static and dynamical aspects of string breaking in a <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi mathvariant="double-struck">Z</mi><mn>2</mn></msub></math> lattice gauge theory coupled to Kogut-Susskind staggered fermions. Using tensor network simulations, we demonstrate that the static potential as well as the site-resolved configuration of the matter sites and gauge links allows us to identify the regimes in which string breaking occurs. Furthermore, we develop a variational quantum eigensolver that allows for reliably preparing the ground state of the theory in both the absence and presence of static charges and to capture the static aspects of the phenomenon. Carrying out state preparation on real quantum hardware for up to 19 qubits, we demonstrate its suitability for current quantum devices. In addition, we study the real-time dynamics of a flux tube between two static charges using both tensor networks and quantum hardware. Using a trotterization for the time-evolution operator, we are able to show that the breaking process starts with the creation of charges inside the string. These eventually redistribute toward the static charges and screen them, which leads to the breaking of the flux tube.

Cyprus

Constantia Alexandrou

Andreas Athenodorou

Kostas Blekos

Georgios Polykratis

Germany

Stefan Kühn

Realizing string breaking dynamics in a <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi mathvariant="double-struck">Z</mi><mn>2</mn></msub></math> lattice gauge theory on quantum hardware

We consider the Chern-Simons theory coupled to massive fundamental matter in three spacetime dimensions, focusing on the Higgsed phase of the bosonic matter in the large-<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>N</mi></math> limit. To study the characteristics of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>Z</mi></math> boson in the Higgsed phase and address an apparent puzzle regarding its fermionic analog, we employ the 3D Bose-Fermi duality to derive the exact large-<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>N</mi></math> result for the two-point function of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>Z</mi></math> boson. We study the spectral representation of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>Z</mi></math> boson and find that, in the large-<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>N</mi></math> limit, it behaves as an unstable resonance with a nonperturbatively large lifetime at weak coupling.

India

Amiya Mishra

Characteristics of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>Z</mi></math> boson in Chern-Simons matter theory

We present a complete classification of domain wall solutions in the two-Higgs-doublet model (2HDM) with a global <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi mathvariant="double-struck">Z</mi><mn>2</mn></msub></math> symmetry, categorized as superconducting, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>C</mi><mi>P</mi></math>-violating, or neither, depending on the scalar particle masses and the ratio of the two Higgs doublets’ vacuum expectation values. We demonstrate that any domain wall solution can be reduced to depend on only six of the eight general field components, with further field reductions possible within different regions of the parameter space. Furthermore, we show that the superconducting solutions can be used to construct stable, current-carrying domain walls in two spatial dimensions. Similarly, the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>C</mi><mi>P</mi></math>-violating solutions allow for two-dimensional configurations where <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>C</mi><mi>P</mi></math> symmetry is locally broken on the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi mathvariant="double-struck">Z</mi><mn>2</mn></msub></math>-symmetric wall, which could provide an out-of-equilibrium environment for <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>C</mi><mi>P</mi></math>-violating processes to occur.

United Kingdom

Richard A. Battye

Steven J. Cotterill

Adam K. Thomasson

Complete classification of domain wall solutions in the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi mathvariant="double-struck">Z</mi><mn>2</mn></msub></math>-symmetric 2HDM

We propose a new scotogenic type model based on a global <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>Z</mi><mn>4</mn></msub></math> symmetry involving dark matter candidates. After the symmetry breaking as <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>Z</mi><mn>4</mn></msub></math> to <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>Z</mi><mn>2</mn></msub></math> via the singlet scalar vacuum expectation value (VEV), the lightest Majorana fermion works as a viable thermal freeze-out dark matter (DM) candidate, and the mass terms for active neutrinos are generated as a finite quantum correction at the one-loop level. A key point of realizing our scotogenic structure is to introduce two types of Majorana fermions (heavy right-handed neutrinos) and inert Higgs doublets with opposite <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>Z</mi><mn>4</mn></msub></math> parities. Since a large VEV for the singlet scalar is not so harmful in an appropriate realization of the Higgs mechanism for the SM gauge symmetry, we can naturally realize a TeV-scale fermionic DM candidate, where constraints via direct detection experiments are less than those for sub-TeV DM. Our scenario involves the Higgs-portal DM interactions, which help the realization of the correct DM relic abundance. Relying on the structure of the model, it is possible to find a natural partner for coannihilation. Our scenario can be investigated via the measurement of the Higgs trilinear self-coupling at the Large Hadron Collider. The simplest way to evade the domain-wall problem, by adding a tiny soft <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>Z</mi><mn>2</mn></msub></math> breaking term, works, keeping a sufficient longevity of the decaying DM lifetime.

Noel Jonathan Jobu

Kenji Nishiwaki

<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>Z</mi><mn>4</mn></msub></math> scotogenic model with a Higgs portal

The proposed Large Hadron electron Collider (LHeC), with a center-of-mass energy of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msqrt><mi>s</mi></msqrt><mo>≈</mo><mn>1.3</mn><mtext> </mtext><mtext> </mtext><mi>TeV</mi></math>, provides a clean and sensitive environment to probe the top quark’s neutral current interactions with the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>Z</mi></math> boson via <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>e</mi><mo>−</mo></msup><mi>p</mi><mo stretchy="false">→</mo><msup><mi>e</mi><mo>−</mo></msup><mi>t</mi><mover accent="true"><mi>t</mi><mo stretchy="false">¯</mo></mover></math>. We investigate the precision with which the Standard Model (SM) <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>t</mi><mover accent="true"><mi>t</mi><mo stretchy="false">¯</mo></mover><mi>Z</mi></math> couplings—the vector and axial-vector components (<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="normal">Δ</mi><msub><mi>C</mi><mrow><mn>1</mn><mi>V</mi></mrow></msub><mo>,</mo><mi mathvariant="normal">Δ</mi><msub><mi>C</mi><mrow><mn>1</mn><mi>A</mi></mrow></msub></math>) can be measured, along with possible new physics effects parametrized by higher-dimensional operators inducing weak electric and magnetic dipolelike interactions (<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>C</mi><mrow><mn>2</mn><mi>V</mi></mrow></msub><mo>,</mo><msub><mi>C</mi><mrow><mn>2</mn><mi>A</mi></mrow></msub></math>). Focusing on the semileptonic decay channel, where either the top quark decays leptonically to a positively charged lepton (<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mo>ℓ</mo><mo>+</mo></msup><mo>=</mo><msup><mi>e</mi><mo>+</mo></msup><mo>,</mo><msup><mi>μ</mi><mo>+</mo></msup></math>) and the antitop hadronically, or vice versa, we utilize the azimuthal angle difference <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="normal">Δ</mi><msub><mi>ϕ</mi><mrow><msup><mi>e</mi><mo>−</mo></msup><msup><mo>ℓ</mo><mo>±</mo></msup></mrow></msub></math> between the scattered electron and the charged lepton <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mo>ℓ</mo><mo>±</mo></msup></math> as the key observable to derive projected constraints. Using a one-parameter multibin <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>χ</mi><mn>2</mn></msup></math> analysis of the differential <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="normal">Δ</mi><msub><mi>ϕ</mi><mrow><msup><mi>e</mi><mo>−</mo></msup><msup><mo>ℓ</mo><mo>±</mo></msup></mrow></msub></math> distribution, the constraints on <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="normal">Δ</mi><msub><mi>C</mi><mrow><mn>1</mn><mi>A</mi></mrow></msub></math> improve from <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="script">O</mi><mo stretchy="false">(</mo><msup><mn>10</mn><mrow><mo>−</mo><mn>1</mn></mrow></msup><mo stretchy="false">)</mo></math> at <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>50</mn><mtext> </mtext><mtext> </mtext><msup><mi>fb</mi><mrow><mo>−</mo><mn>1</mn></mrow></msup></math> to <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="script">O</mi><mo stretchy="false">(</mo><msup><mn>10</mn><mrow><mo>−</mo><mn>2</mn></mrow></msup><mo stretchy="false">)</mo></math> at <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>1000</mn><mtext> </mtext><mtext> </mtext><msup><mi>fb</mi><mrow><mo>−</mo><mn>1</mn></mrow></msup></math>, while the improvement for <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="normal">Δ</mi><msub><mi>C</mi><mrow><mn>1</mn><mi>V</mi></mrow></msub></math> remains within the same order of magnitude, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="script">O</mi><mo stretchy="false">(</mo><msup><mn>10</mn><mrow><mo>−</mo><mn>1</mn></mrow></msup><mo stretchy="false">)</mo></math>. These results correspond to average relative precisions of approximately 8% and 68%, respectively, with respect to their SM values. The anomalous tensor couplings <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>C</mi><mrow><mn>2</mn><mi>V</mi></mrow></msub></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>C</mi><mrow><mn>2</mn><mi>A</mi></mrow></msub></math> are constrained at the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="script">O</mi><mo stretchy="false">(</mo><msup><mn>10</mn><mrow><mo>−</mo><mn>1</mn></mrow></msup><mo stretchy="false">)</mo></math> level even at low luminosity and improve moderately with increasing luminosity. While the two-parameter analysis broadens the allowed regions due to parameter correlations, it maintains competitive sensitivity, particularly for the SM-like couplings. Throughout, we assume a systematic uncertainty of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>δ</mi><mi>s</mi></msub><mo>=</mo><mn>5</mn><mo>%</mo></math> in all analyses, and all results are quoted at the 95% confidence level. These results demonstrate the LHeC’s potential to provide complementary and competitive sensitivity to top-<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>Z</mi></math> couplings compared to current and future hadron and lepton collider capabilities.

South Africa

Katlego Machethe

Pramod Sharma

Mukesh Kumar

Brazil

Rafiqul Rahaman

Bruce Mellado

Analyzing <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>t</mi><mover accent="true"><mi>t</mi><mo stretchy="false">¯</mo></mover><mi>Z</mi></math>-couplings at the future <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>e</mi><mo>−</mo></msup><mi>p</mi></math> collider

Astrophysical evidence has hinted at the existence of a nonzero NUT charge, which breaks the $$\mathbb {Z}_2$$ symmetry of spacetime and induces novel features in geodesics. In this work, we investigate the Lense–Thirring precession of the spherical orbits in the Kerr–Taub–NUT spacetime, with particular emphasis on its connection to recent observations of black hole jet precession. We analyze the reflection symmetry breaking in trajectories of the spherical orbits and extract their precession angular velocity. It is worth noting that in the absence of spin, the spherical orbits reduce to tilted circular orbits without precession, whereas for nonzero spin, the precession angular velocity increases with the absolute value of the NUT charge. We then model the motion of particles near the warp radius of a tilted accretion disk using the spherical orbits and constrain the black hole parameter space based on the observed jet precession of M87*. The results indicate that regions with low spin and large NUT charge were excluded, and that the jet precession measurements cannot distinguish the sign of the NUT charge. The excluded region is larger for retrograde accretion disks than for prograde ones. We also find that this observation do not allow a clear distinction between black holes and naked singularities. Moreover, we also explore how black hole parameters influence the structure of accretion disk. These results have important theoretical and astronomical significance for us to deeply understand NUT space-time.

China

Xiang-Cheng Meng

Shan-Ping Wu

Shao-Wen Wei

Precession of spherical orbits for the spacetime without $$\mathbb {Z}_2$$ symmetry induced by NUT charge

In the present work, we study the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>Z</mi><mrow><mi>c</mi><mi>s</mi></mrow><mo>+</mo></msubsup></math> exotic state production in the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>B</mi><mo>+</mo></msup></math> meson decays through the meson loop mechanism, where the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>B</mi><mo>+</mo></msup></math> meson decays into an anticharmed meson and a charmed-strange meson pair, and consequently couples to <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>Z</mi><mrow><mi>c</mi><mi>s</mi></mrow></msub></math> and a light meson (<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>ϕ</mi><mo>,</mo><msup><mi>ρ</mi><mn>0</mn></msup><mo>,</mo><mi>ω</mi><mo>,</mo><mi>η</mi><mo>,</mo><msup><mi>η</mi><mo>′</mo></msup></math>, and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>π</mi><mn>0</mn></msup></math>) via exchanging a proper charmed or charmed-strange meson. Using the effective Lagrangian approach, we estimate the branching fractions of different channels, finding them to be of the order of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mn>10</mn><mrow><mo>−</mo><mn>4</mn></mrow></msup></math>, and their ratios are almost independent of the model parameter. The fit fractions of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>Z</mi><mrow><mi>c</mi><mi>s</mi></mrow><mo>+</mo></msubsup></math> in different <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>B</mi><mo>+</mo></msup></math> decay processes are also estimated, and we propose searching for <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>Z</mi><mrow><mi>c</mi><mi>s</mi></mrow><mo>+</mo></msubsup></math> in the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>B</mi><mo>+</mo></msup><mo stretchy="false">→</mo><mi>J</mi><mo>/</mo><mi>ψ</mi><msup><mi>K</mi><mo>+</mo></msup><msup><mi>η</mi><mo>′</mo></msup></math> process, which should be accessible to both Belle II and LHCb Collaborations.

Zhuo Yu

Qi Wu

Dian-Yong Chen

<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>Z</mi><mrow><mi>c</mi><mi>s</mi></mrow><mo>+</mo></msubsup></math> production in <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>B</mi><mo>+</mo></msup></math> decays

A complete assessment of any dark matter model requires confronting its low-energy phenomenology with its high-scale theoretical viability. We undertake such a dual analysis for a class of two-component scalar dark matter models stabilized by $$\mathbb {Z}_{2n}$$ symmetries, specifically the $$\mathbb {Z}_4$$ , $$\mathbb {Z}_6(23)$$ , and $$\mathbb {Z}_6(13)$$ frameworks. Each model is tested against the latest observational data, including the Planck relic abundance and stringent direct detection limits from the LUX-ZEPLIN (LZ) experiment. Simultaneously, we evaluate their theoretical integrity up to the GUT and Planck scales by enforcing vacuum stability and perturbative unitarity with one-loop Renormalization Group Equations. This combined approach reveals a rich and varied landscape of possibilities. We demonstrate that the $$\mathbb {Z}_4$$ model offers a broadly viable parameter space sustained by efficient semi-annihilation. In stark contrast, the $$\mathbb {Z}_6(13)$$ scenario is shown to be highly fine-tuned, with solutions confined to the Higgs resonance. Our most significant finding concerns the $$\mathbb {Z}_6(23)$$ model: we show that an apparent conflict between experimental data and high-scale consistency is resolved when the model is viewed as an effective field theory, yielding a concrete prediction for new physics at or below the $$10^6$$ GeV scale. This work provides a definitive guide to the viability of these $$\mathbb {Z}_{2n}$$ scenarios and serves as a compelling demonstration of how high-energy consistency checks can yield crucial insights into the nature of dark matter.

J. Carvalho-Corrêa

I. Pereira

B. Sánchez-Vega

A. Viglioni

Theoretical and experimental constraints on $$\mathbb {Z}_{2n}$$ multi-component dark matter models

We numerically study <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msub><mrow><mi mathvariant="double-struck">Z</mi></mrow><mrow><mi>N</mi></mrow></msub></mrow></math> lattice gauge theories in 4D as prototypical models of systems with <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi mathvariant="double-struck">Z</mi><mi>N</mi></msub></math> 1-form symmetry. For <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>N</mi><mo>≥</mo><mn>3</mn></mrow></math>, we provide evidence that such systems exhibit not only the expected phases with spontaneously broken/restored symmetry but also a third photon phase. When present, the 1-form symmetry provides a precise notion of confinement, and it is commonly believed that confinement ensues due to the proliferation of extended, stringlike objects known as center vortices, which carry a <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi mathvariant="double-struck">Z</mi><mi>N</mi></msub></math> flux. However, this picture is challenged by the three-phase scenario investigated here. We show that both the confined and the photon phases are associated with the proliferation of center vortices and that the key difference between them lies in whether or not vortex junctions—the monopoles— proliferate.

Jeffrey Giansiracusa

David Lanners

Tin Sulejmanpasic

Emergent Photons and Confinement: A Numerical Study on <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msub><mrow><mi mathvariant="double-struck">Z</mi></mrow><mrow><mi>N</mi></mrow></msub></mrow></math> Lattice Gauge Theory

We explore the potential to detect the <math altimg='si39.svg'><mrow><mi>U</mi><msub><mrow><mo>(</mo><mn>1</mn><mo>)</mo></mrow><mrow><msub><mi>L</mi><mi>&#956;</mi></msub><mo>&#8722;</mo><msub><mi>L</mi><mi>&#964;</mi></msub></mrow></msub></mrow></math> model featuring triplet scalars &#916; at the <italic>&#956;</italic>TRISTAN collider. The new gauge boson <italic>Z</italic>&#8242;, arising from the spontaneous breaking of <math altimg='si39.svg'><mrow><mi>U</mi><msub><mrow><mo>(</mo><mn>1</mn><mo>)</mo></mrow><mrow><msub><mi>L</mi><mi>&#956;</mi></msub><mo>&#8722;</mo><msub><mi>L</mi><mi>&#964;</mi></msub></mrow></msub></mrow></math>, can exhibit maximal flavor changing interactions under the exchange symmetry, while &#916; mediates the flavor conserving interactions. The absence of muon <math altimg='si6.svg'><msub><mrow><mo>(</mo><mi>g</mi><mo>&#8722;</mo><mn>2</mn><mo>)</mo></mrow><mi>&#956;</mi></msub></math> can be explained by interference effects arising from opposite contributions of <italic>Z</italic>&#8242; and &#916;, with similar interference patterns also manifesting in the tau decay process <math altimg='si7.svg'><mrow><mi>&#964;</mi><mo>&#8594;</mo><mi>&#956;</mi><mi>&#957;</mi><mover accent='true'><mi>&#957;</mi><mo>&#175;</mo></mover></mrow></math>. These counteracting effects render the model phenomenologically interesting and warrant further investigation. For the mass <math altimg='si22.svg'><msub><mi>m</mi><msup><mi>Z</mi><mo>&#8242;</mo></msup></msub></math> in the range of hundreds of GeV, we find that <math altimg='si30.svg'><mrow><msup><mi>&#956;</mi><mo>+</mo></msup><msup><mi>&#956;</mi><mo>+</mo></msup></mrow></math> and <math altimg='si35.svg'><mrow><msup><mi>&#956;</mi><mo>+</mo></msup><msup><mi>e</mi><mo>&#8722;</mo></msup></mrow></math> collider at the <italic>&#956;</italic>TRISTAN can probe many regions inaccessible to current experiments and offer greater projected sensitivity than opposite-sign muon colliders. This suggests that <italic>&#956;</italic>TRISTAN can serve as complementary exploration to the <math altimg='si39.svg'><mrow><mi>U</mi><msub><mrow><mo>(</mo><mn>1</mn><mo>)</mo></mrow><mrow><msub><mi>L</mi><mi>&#956;</mi></msub><mo>&#8722;</mo><msub><mi>L</mi><mi>&#964;</mi></msub></mrow></msub></mrow></math> model, providing compelling motivation for the next generation of high-energy lepton colliders.

Fei Huang

South Korea

Jin Sun

Probing maximal flavor changing <italic>Z</italic>&#8242; in <math altimg='si39.svg'><mrow><mi>U</mi><msub><mrow><mo>(</mo><mn>1</mn><mo>)</mo></mrow><mrow><msub><mi>L</mi><mi>&#956;</mi></msub><mo>&#8722;</mo><msub><mi>L</mi><mi>&#964;</mi></msub></mrow></msub></mrow></math> at <italic>&#956;</italic>TRISTAN